Energy-based Potential Games for Joint Motion Forecasting and Control (2312.01811v1)

Abstract: This work uses game theory as a mathematical framework to address interaction modeling in multi-agent motion forecasting and control. Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces challenges such as unknown game parameters. To tackle these, we establish a connection between differential games, optimal control, and energy-based models, demonstrating how existing approaches can be unified under our proposed Energy-based Potential Game formulation. Building upon this, we introduce a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. The analysis provides empirical evidence that the game-theoretic layer adds interpretability and improves the predictive performance of various neural network backbones using two simulations and two real-world driving datasets.

• The paper introduces Energy-based Potential Games (EPOs) that combine differential games, optimal control, and energy-based models for joint motion forecasting and control.
• It presents a novel differentiable optimization layer integrated with neural networks that significantly improves predictive performance and interpretability.
• Empirical results on synthetic and real-world datasets demonstrate enhanced accuracy in standard metrics such as minADE and minFDE compared to baselines.

Energy-Based Potential Games for Joint Motion Forecasting and Control

The paper "Energy-based Potential Games for Joint Motion Forecasting and Control" introduces a novel framework that unifies differential games, optimal control strategies, and energy-based models (EBMs) to address the challenges of multi-agent interaction modeling, particularly for self-driving vehicles (SDVs). The authors successfully create a cohesive theoretical and practical structure to handle game-parameter inference and differentiable optimization within the field of multi-agent systems.

Summary of Contributions

1. Unified Theoretical Framework: The paper bridges differential games and optimal control with EBMs. Previously, these domains were leveraged independently for robotics applications. By integrating game theory with EBMs, the authors propose Energy-based Potential Games (EPOs), which frame multi-agent interactions under a single optimization problem.
2. Differentiable Optimization Layer: A novel differentiable Energy-based Potential Game Layer (EPOL) is introduced. This layer integrates seamlessly with neural networks, combining explicit initialization strategies with implicit game-theoretic optimization, improving both interpretability and predictive performance.
3. Empirical Validation: The proposed methods are validated using both synthetic (RPI dataset) and real-world datasets (exiD and Waymo Interactive). The experimental results demonstrate significant improvements in metrics such as minADE, minFDE, minSADE, and minSFDE, compared to several state-of-the-art baseline methods.

Technical Implementation

System Architecture

The system architecture comprises several key components:

• Observation Encoding: Historical agent trajectories and map features are encoded using a vectorized representation processed by hierarchical graph neural networks.
• Decoding of Game Parameters: Multi-modal weights and initial strategies are predicted via MLP-based decoders. These parameters serve as inputs for game-theoretic energy minimization.
• Differentiable Optimization: The EPOL leverages a Nonlinear Least Square solver to achieve parallel optimization, ensuring that the system remains tractable even as the number of prediction modes increases.
• Training Objectives: Training utilizes a multi-task loss function, including terms for imitation, goal achievement, and probability prediction, which improves overall model performance and interpretability.

Evaluation and Results

The evaluation spans across different benchmarks and experimental setups:

• Highway Merging and Intersection Scenarios: The proposed model yields accurate joint predictions that reflect various plausible future trajectories, while also exhibiting lower error margins in sequence-level metrics. This is particularly evident in the exiD dataset results, where the method outperforms baselines in scene-level accuracy metrics.
• Simulated Multi-Agent Interactions: On the RPI dataset, which includes diverse multi-modal demonstrations, the method showcases its ability to differentiate between various agent interactions effectively.

Implications for AI Development

The integration of EBM learning techniques into game-theoretic frameworks paves the way for more interpretable AI models in autonomous driving and robotics applications. By enabling end-to-end learning and optimization, the approach ensures that future joint state predictions are both accurate and interpretable. Further implications include:

• Enhanced Predictive Control: The approach allows for real-time adjustments based on predicted trajectories, making it suitable for real-world deployment in dynamic environments.
• Improved Safety and Robustness: By directly modeling interactions and incorporating game-theoretic principles, the system is expected to handle uncertain and adversarial scenarios more gracefully.

Future Directions

The work opens several avenues for future research:

• Scalability Enhancements: While the current implementation scales well with mode numbers, improvements can streamline performance for scenarios with many interacting agents.
• Dynamic Agent Identification: Methods to dynamically identify and focus on relevant interacting agents can further enhance efficiency.
• Combining with Raw-Sensor Data: Extending the approach to handle raw sensor data, thus integrating perception with planning, could lead to even more robust systems.
• Advanced Safety Constraints: Incorporating more sophisticated vehicle geometry approximations and continuous evaluation of collision avoidance could provide further improvements in predictive accuracy and safety.

Conclusion

"Energy-based Potential Games for Joint Motion Forecasting and Control" offers a significant contribution to the field of AI and robotics. By unifying differential games with energy-based models and introducing an efficient differentiable optimization layer, the authors not only advance the state-of-the-art in motion forecasting but also open new possibilities for interpretable and robust multi-agent systems. The empirical results solidify its practical applicability, making it a promising approach for a wide range of applications in autonomous driving and beyond.